Adjustment of an Inverse Matrix Corresponding to a Change in One Element of a Given Matrix

By J. Sherman, Winifred J. Morrison. 1950

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Citations in the corpus

Information-theoretic Online Memory Selection for Continual Learning (2022, positive): “Fortunately, since AM+ differ with AM by a rank-one matrix, its inverse can be computed efficiently given A−1M according to the Sherman-Morrison Formula (Sherman & Morrison, 1950), A−1M+ = A −1 M − A−1Mh?h > ?”
GradientDICE: Rethinking Generalized Offline Estimation of Stationary Values (2020, methodology): “Using the Sherman-Morrison formula (Sherman & Morrison, 1950), it is easy to verify w ∗ ,ξ = w ∞ ,ξ .”
Deep Equilibrium Models (2019, methodology): “We propose to address this using Broyden’s method [10], a quasi-Newton approach that makes low-rank updates to approximate J − 1 g θ via the Sherman-Morrison formula [42]: where ∆ 1: T and ∆ g 1: T ; x 1: T ) .”
A Generalized Input-Output Multiplier Calculus for Australia (2001, methodology): “Based on early work by Sherman and Morrison (1950), Bullard and Sebald develop a technique for estimating uncertainties by identifying important parameters.”
Fast Direct Methods for Gaussian Processes (2014, methodology): “Thankfully, there has recently been tremendous progress in obtaining fast low-rank factorizations of matrices.”
Graph Learning From Data Under Laplacian and Structural Constraints (2016, methodology): “After adding a scalar value ν to (Θ)ii, we use the Sherman-Morrison formula [51] to update C as”
What learning algorithm is in-context learning? Investigations with linear models (2022, methodology): “However, one can exploit the Sherman–Morrison formula (Sherman & Morrison, 1950) to reduce the inverse to a sequence of rank-one updates performed example-by-example.”
The NANOGrav 11 Year Data Set: Pulsar-timing Constraints on the Stochastic Gravitational-wave Background (2018, methodology): “In this paper, we include ECORR noise as block-diagonal entries (one block per epoch per backend–receiver system) in the otherwise diagonal white-noise covariance matrix, and invert the matrix using the fast Sherman & Morrison (1950) formula.”
Locality Sensitive Sparse Encoding for Learning World Models Online (2024, methodology): “Though W t +1 can be re-cursively updated using Sherman-Morrison formula (Sherman & Morrison, 1950) as done in Least-Squares TD (Bradtke & Barto, 1996), when the feature becomes very high-dimensional to gain expressiveness, it can become inefficient or even impractical.”
An algorithm for solving the absolute value equation (2009, methodology): “The first of them is the Sherman-Morrison formula ((iii) below) and the Sherman-Morrison determinant formula ((i) below), see [14].”
Recursive Least Squares for Training and Pruning Convolutional Neural Networks (2022, methodology): “By using Sherman-Morrison matrix inversion formula [20], we can easily get”
Markowitz Revisited: Mean-Variance Models in Financial Portfolio Analysis (2001, unknown): “The Sherman–Morrison–Woodbury formula [187, 204] applied to Σ̃ = Σ + r̄r̄∗ yields Σ̃−1 = Σ−1 − Σ −1r̄r̄∗Σ−1 1 + r̄∗Σ−1r̄ = Σ−1 − Σ −1r̄r̄∗Σ−1 1 + γ .”
Revisiting Stein's paradox: multi-task averaging (2014, methodology): “The Sherman-Morrison formula (Sherman and Morrison, 1950) can be used to find the inverse: (Z − z1>)−1 = Z−1 + Z −1z1>Z−1 1− 1>Z−1z .”
Active learning of linearly parametrized interatomic potentials (2016, methodology): “When A changes, it also takes O ( m 2 ) operations to update A − 1 using the Sherman-Morrison [38] rank-one update.”
Random Forests for dependent data (2020, unknown): “Hence, using a version of Sherman–Morrison–Woodbury identity in [64], we have with c−1 := (V ol(C1), V ol(C2), · · · , V ol(Cg(k)+1)), ( lim n→∞ 1 n Z>QZ )−1 = α−1diag(c−1)− α−2diag(c−1) (∑q j 6=j′=0 ρjρj′ ) cc>diag(c−1) 1 + α−1 (∑q j 6=j′=0 ρjρj′ ) c>diag(c−1)c = α−1diag(c−1)− α−1 (∑q j 6=j′=0 ρjρj”
Efficient leave-one-out cross-validation of kernel fisher discriminant classifiers (2003, methodology): “…cross-validation procedure can then be written in closed form as The i th element of r ( i ) is given by kernel Fisher discriminant (KFD) [1], radial basis function (RBF) [35], Ad-aBoost (AB) [34] and regularised AdaBoost (AB R ) [32] classiﬂers on 13 different benchmark datasets [33].”